You might want to do several things. For sure get it in writing what they will do for you (including price) and include something to cover you if it gets lost, stolen, or damaged. If you drop it off in person, get a receipt signed by them to authenticate delivery.
What may be a better delivery option is to take it to a "pack and ship" business and have them professionally pack it and with delivery by a major company (like FedEx, UPS) that gives you delivery confirmation along with a signature of who it was delivered to. Insurance for the delivery trip should also be purchased for the full value. What this will give you is 1) someone to testify to the condition of the item, how it was packed, etc. 2) someone to testify that it was infact delivered, when, and to whom.
Think about all of the steps in the process and what you can do to protect yourself on each of them. Remember though that an independent and professional business stating something is probably worth more to the court than you saying you did something (video showing you did will help, but could be argued to have been rigged to show something that didn't actually happen). Things will most likely go well regardless, but if you're worried now, take steps now to cover this worry as well as help you make your case if things do go badly and end up in court.